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arXiv · 2604.27782

Explicit Quantum Search Algorithm for the Densest k-Subgraph Problem

Yu. A. Biriukov·R. D. Morozov·I. V. Dyakonov·S. S. Straupe
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Abstract

This paper addresses the problem of finding the densest $k$-vertex subgraph in an arbitrary graph. This problem is NP-hard and has important applications in social network analysis, fraud detection, recommendation systems, and bioinformatics. We propose two quantum approaches to solve this problem: reduction to Quadratic Unconstrained Binary Optimization (QUBO) and using Grover's quantum search algorithm. For the latter approach, we present an explicit gate-based oracle circuit utilizing Dicke states and Quantum Fourier Transform for edge counting. Numerical simulations demonstrate a quadratic speedup over classical Brute-force search.

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Yu. A. Biriukov, R. D. Morozov, I. V. Dyakonov, S. S. Straupe. 2026-04-30. Explicit Quantum Search Algorithm for the Densest k-Subgraph Problem. https://arxiv.org/abs/2604.27782

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